1. Field of the Invention
The present invention relates to a device and method for performing adaptive equalization in a communications system. In particular, the present invention provides for blind or referenced trained adaptive equalization for use in digital communication systems.
2. Description of the Prior Art
In communications systems multiple reflections lead to a confluence at a receiver of several signals which all stem from the same signal generated at a transmitter but differ in arrival time, carrier phase and amplitude. This can impair the transmission performance and cause fading or even signal elimination at the receiver. These so-called multipath effects particularly appear in urban environments which are at the same time those areas with the highest demand for communication systems. The relative motion of the receiver with respect to the transmitter and/or the transmitter with respect to the receiver can cause a doppler effect which can cause fading which also impairs transmission performance. These effects are particular troublesome with mobile communication systems. Mobile channels are generally characterized as fading multipath channels with time dispersion (multipath spreads). The mobility of such systems creates transmission channel characteristics that are constantly changing as the geometries, transmission path, interference and transmission medium change.
The high bit or data rates of modern digital mobile radio systems cause a significant part of the typical multipath effects to appear as inter-symbol interference (ISI). Because of the non-ideality of the frequency response of the transmission channel, each transmitted symbol interferes with the others, generating ISI. To remove the inter-symbol interference, the systems are usually equipped with equalizers (see Lucky R. W., "Automatic equalization for digital communication", Bell System Technical. Journal, 1965, 44, pp. 574-588). Equalizers are widely used in communications systems and can employ either dedicated hardware or a programmable digital signal processors (DSP) or DSPs. There are two primary types of equalizers: linear and non-linear. Both types of equalizers can be classified as either reference trained or blind. Both types of equalizers typically utilize an adaptive filter. The adaptive filter, often referred to as transversal filter or moving average filter, is made with a chain of delay elements, at the output of each of which is placed a variable gain amplifier (tap gain). The variable tap gains are usually referred to as adjustable coefficients. The outputs of the variable tap gain amps are then added to provide a signal sample which gives an indication of the transmitted symbol. This signal sample is then sent to a decision element or symbol detector to obtain a decided symbol. Assuming no errors, the decided symbol should be equal to the symbol fed into the transmission channel by the transmitter.
By appropriate selection of the delay elements and the coefficients, equalizers can reduce the inter-symbol interference according to a given criterion. Some types of equalizers, referred to as adaptive, provide for automatic coefficient adjustment. In these equalizers, starting from arbitrary initial coefficients often quite far from the optimum, the coefficients can be modified iteratively until an optimal configuration is reached. To minimize inter-symbol interference many adaptive equalization systems adopt the criterion of minimizing the mean square error (MSE) defined from the signal samples at the adaptive filter output before the decision element and the corresponding transmitted signals using estimated gradient methods. For a given transmission channel, the mean square error is a quadratic function of the tap gains for referenced trained adaptive filters. The mean square error is minimized by estimating its gradient with respect to the filter coefficients. The filter coefficients are modified in the direction opposite to the estimated gradient.
More particularly, starting from arbitrary tap gain values, differences are found between the transmitted reference symbols and the signal samples at the equalizer output. Using these differences, in combination with the signals present at the equalizer input, the tap gains are modified to obtain the minimum mean square error. It can be shown that a tap gain configuration which minimizes the mean square error exists and is unique (see Gersho A., "Adaptive equalization of highly dispersive channels for data transmission", Bell System Technical Journal, 1969, 48, pp. 55-70). When the optimum configuration has been reached the outputs of the receiver decision element, i.e. the self-decided symbols, are correct with very high probability and can be used instead of the reference symbols to obtain the present value of the error to be used in the adaptation process. Many other coefficient adjustment schemes have been suggested. The basic assumption for the adaptive equalizer is therefore that the current output samples for the adaptive equalizer can be compared with the corresponding transmitted symbols, which have to be known a priori.
However, if the channel characteristics change during transmission, as is particularly the case with mobile systems, the self-decided symbols may become incorrect and the equalizer is unable to reconfigure the tap gains to the new optimum values. In this case, to obtain reliable self-decided symbols at the receiver output, the above described start-up procedure ( i.e., the transmitted reference sequence and adjustment of the coefficient) must be repeated with considerable loss of time. To remedy this serious drawback, blind equalization techniques have been proposed. Blind equalization techniques are capable of converging in a configuration of limited distortion without the necessity of using a predetermined reference symbol sequence (see Y. Sato, "A method of self-recovering equalization for multi-level amplitude-modulation systems", IEEE Transaction on Communication, Vol. COM-23, N. 6, pp. 679-682, June 1975; D. N. Godard, "Self-recovering equalization and carrier tracking in two-dimensional data communication systems", IEEE Transaction on Communication, Vol. COM-28, N. 11, pp. 1867-1875, November 1980; A. Benveniste and M. Goursat, "Blind equalizers", IEEE Transaction on Communication, Vol. COM-32, N. 8, pp. 871-883, August 1984).
To minimize inter-symbol interference these blind techniques typically use new non-convex cost functions different than the mean square error used for the self-learning equalizer. Under weak conditions, these cost functions characterize the inter-symbol interference sufficiently well while their stochastic minimization can be performed by using locally generated control signals with no knowledge of the transmitted data. However, these methods of adaptive blind equalization are not fully satisfactory because they do not converge smoothly, and particularly because under steady state operating conditions they maintain a very high residual variance of the error signal. In other words, they do not reach the point of minimal inter-symbol interference but oscillate continually around the minimum. This leads to operation with unacceptable results.
Blind equalization techniques are attractive not only because they provide for uninterrupted data transmission (because there is no need to send a training sequence when incorrect decisions are made or the transmission channel characteristics change) but, also because they are quite easy to implement in practice. Most of the existing blind equalization techniques can be categorized as decision-directed-type techniques which use a nonlinear estimator at the output of the equalizer to generate a decision-directed estimated error. This error is then utilized to adjust the coefficients in a feed forward filter. Thus, the decision directed type equalizer uses a feed forward filter to compensate for the non-ideal channel. However, a feed forward filter is not very effective in equalizing channels containing spectral nulls. In an attempt to compensate for the channel distortion, the equalizer places a large gain in the vicinity of the spectral null and as a consequence significantly enhances the additive noise present in the received signal. Consequently, decision directed blind equalizers are not effective for equalizing channels containing spectral nulls. Spectral nulls in the transmission channel are encountered in practice wherever there is multipath propagation. Mobil radio channels, as discussed above, are generally characterized as fading multipath channels with time dispersion (multipath spreads). The ability of the equalizer to compensate for spectral nulls is particularly important where multi-path propagation is present.
Additionally, a decision directed equalizer does not efficiently compensate for postcursor ISI. Postcursor ISI is the effect of previously detected symbols on the present symbol. Because detected symbols are not used as feedback, the effect of ISI from previously detected symbols is not effectively removed from the present estimate. The decision directed equalization with a feedforward filter attempts to invert the transmission channel without directly using previously detected symbols.
Decision feedback equalization techniques use feedback to provide for better compensation for spectral nulls and attempt to eliminate postcursor ISI. Decision feedback equalization permits the removal of ISI by using decision feedback to cancel from the present symbol the interference from symbols which have already been detected. The basic idea of decision feedback equalization is that if the value of symbols already detected are known then the ISI contributed by these symbols in the present symbol can be determined and canceled exactly by subtracting the previously detected symbol values with appropriate weighing. A typical decision feedback equalizer combines the output of a feed forward filter and feedback filter, and provides the combined outputs to a decision element. The output of the decision element is then utilized by the feedback filter. The output of a feedback filter can be thought of as representing the postcursor ISI imposed by previously detected symbols on the present symbol.
The adjustment of the feed forward filter and feedback filter are typically based on the current value of the filter coefficients and an objective function. The objective function typically uses an error signal which can be defined as the difference between the symbol sequence input to the decision element and the output symbol sequence of the decision element. Because the error signal is based upon the output sequence and the output sequence is used as input to the feedback filter, decision feedback equalizers are susceptible to decision error propagation. Decision error propagation can cause the equalizer to "blow up", diverge or oscillate.
The problem of decision error propagation can be explained as follows, if the decision element incorrectly decides (or detects or assigns) a symbol this incorrect symbol is provided to the feedback filter as input. It should be noted that this incorrect decision will then be utilized by the feedback filter to compensate for postcursor ISI for a number of present symbols (the exact number will depend upon the number of delay elements in the feedback filter). The incorrect determination by the decision element not only impacts the symbols provided to and propagated in the feedback filter but, also impacts the error signal which is utilized by the feedback filter to adjust its coefficients. The incorrect adjustment of the coefficients along with the incorrect symbols used by the feedback filter causes an incorrect cancellation to be made from the present symbol (i.e., the postcursor ISI from previously detected symbols is incorrectly determined). The sequence provided to the decision element is thus incorrect and the decision element is more likely to make another incorrect decision. This cycle repeats. In severe cases decision error propagation can cause the equalizer to diverge rather than converge. Thus, the decision error propagates through the equalizer resulting in the equalizer not minimizing the ISI.
One proposed solution to reduce the effects of decision error propagation is to provide a reliability criterion for the self-decided symbols that prevents updating of the adjustable coefficients when the reliability criterion is low. (See U.S. Pat. No. 4,847,797 entitled Adaptive Blind Equalization Method and Device, to Picchi et. al.) Thus a binary consent function prevents the equalizer from updating the adaptive coefficients. This technique requires the additional complexity of a consent or inhibit function. It also prevents the equalizer from tracking changes in the transmission channel when the reliability criterion is low. The propagation error still exists but, the binary consent function allows adaptation to proceed when the propagation error is small and stops adaptation when the propagation error is large. Thus, this technique only stops adaptation and not the propagation error.